Resolution of singularities
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For the technique used for graph C*-algebras and Leavitt path algebras, see Graph C*-algebra § Desingularization.
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964;[1] while for varieties of dimension at least 4 over fields of characteristic p, it is an open problem.[2]